Abstract
We consider the unit root testing problem with errors being nonlinear transforms of linear processes. When the linear processes are long-range dependent, the asymptotic distributions in the unit root testing problem are shown to be functionals of Hermite processes. Functional limit theorems for nonlinear transforms of linear processes are established. The obtained results differ sharply from the classical cases where asymptotic distributions are functionals of Brownian motions.The author thanks the referee and Professor B. Hansen for their valuable suggestions. The work is supported in part by NSF grant DMS-04478704.
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